Redox Coupling Electron Transfer

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Reversible redox energy coupling inelectron transfer chainsArtur Osyczka1*, Christopher C. Moser1, Fevzi Daldal2 & P. Leslie Dutton1

1The Johnson Research Foundation, Department of Biochemistry and Biophysics, and2Department of Biology, Plant Science Institute, University of Pennsylvania,

Philadelphia, Pennsylvania, 19104, USA

* Permanent address: Jagiellonian University, Faculty of Biotechnology, Krakow, Poland

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Reversibility is a common theme in respiratory and photosynthetic systems that couple electron transfer with a transmembraneproton gradient driving ATP production. This includes the intensely studied cytochromebc1, which catalyses electron transferbetween quinone and cytochrome c. To understand how efficient reversible energy coupling works, here we have progressivelyinactivated individual cofactors comprising cytochrome bc1. We have resolved millisecond reversibility in all electron-tunnellingsteps and coupled proton exchanges, including charge-separating hydroquinonequinone catalysis at the Qo site, whichshows that redox equilibria are relevant on a catalytic timescale. Such rapid reversibility renders popular models based on asemiquinone in Qo site catalysis prone to short-circuit failure. Two mechanisms allow reversible function and safely relegateshort-circuits to long-distance electron tunnelling on a timescale of seconds: conformational gating of semiquinone for bothforward and reverse electron transfer, or concerted two-electron quinone redox chemistry that avoids the semiquinoneintermediate altogether.

The challenge of engineering efficient photosynthetic and respira-tory energy conversion is to favour productive electron and protontransfer reactions that generate or use membrane proton motiveforce (DmH), while suppressing energy-wasting short-circuit reac-tions. Photosynthetic reaction centres favour productive light-induced charge separation and avoid wasteful charge-recombiningshort-circuits by expending much of the absorbed light energy todrive the forward charge-separating steps, and thereby slow thereverse uphill charge returns that make short-circuits more likely.

For other crucial membrane energy-coupled oxidoreductases,

such as the cytochromebc1andb6ffamily, the modest driving forceprovided by substrates makes this strategy impossible.Furthermore,as DmH builds up, the net reaction can be reversed, as shown inmitochondrialcytochromebc1 andcomplexI by classic experimentsthat artificially added ATP to increase DmH and to stimulatereverse electron flow1,2 on a timescale of minutes. Some litho-trophic organisms apparently rely on the reverse electron flowthrough cytochromebc1for growth

3,4. Despite these observations,contemporary models for energy conversion in cytochrome bc1(refs 516) neglect reverse reactions and the implications of rever-sibility on short-circuit vulnerability. These models fail if reversi-bility on a rapid catalytic timescale is fully proven.

Here we have used photosynthetic membranes of the bacteriumRhodobacter capsulatus to investigate cytochromebc1 reversibility.R. capsulatusprovides the kinetic means for rapid, light-activated

delivery of the substrates hydroquinone (QH2) and oxidizes cyto-chrome c to cytochrome bc1 (Fig. 1a), even as the cofactors areprogressively knocked out genetically. This strategy avoids long-standing difficulties in resolving concurrent reactions in theb-chain (comprising haem b L, haem b Hand the quinone of theQisite) and the c-chain (comprising the iron-sulphur centre FeS,haem c1 and cytochrome c(mostlyc2 but also cy)). This strategy alsoestablishes a rigorous single-turnover activation of cytochromebc1to oxidize and reduce only one quinone molecule at the Qo site,where the Q pool and the b- and c-chains meet and where energyconversion is catalysed.

Drawing on substrate and cofactor redox midpoint potentialsand their pH dependencies (Fig. 1b), we have exposed selectedsingle-turnover cofactor knockout systems to a range of drivingforces from exergonic to endergonic (Fig. 1c) to define, step by step,

the thermodynamic parameters and to reveal the timescale ofreversibility of the operating cytochromebc1.

Electron transfer in cofactor knockouts

Figure 2 presents the flash-activated haem b reduction kinetics incytochromebc1with different combinations of cofactor knockouts.The system is initially poised at high redox potentials to oxidize theQ pool. The uninhibited wild-type system (Fig. 2a, black) monitorsflash-generated QH2 arriving at the Qo site and the 8-ms concurrentreductionof both FeS andhaembL, followed by rapid haem bL to bH

electron transfer across the membrane. Subsequent reduction of Qito semiquinone by haembHcompletes the electrical charging of themembrane (Fig. 1a).

After reduction, FeS normally undergoes constrained diffusion totransfer the electron to haem c1 (refs 1719). In turn, haem c1reduces cytochromec (data not shown). Antimycin eliminates Qifunction (Fig. 2a, green), so that the electron advances only as far ashaem bH to reveal its full reduced extent. There is no noticeableeffect of inactivation of the Qi siteon the rateof Qo site turnover andhaembHreduction. Further addition of myxothiazol (Fig. 2a, red)inhibits QoH2 oxidation in thefirst place andno haem b reductionisobserved; this rules out any other routes to haemb reduction inthese experiments.

In the first cofactor knockout (Fig. 2b), mutation of the meth-ionine ligand of haem c1 to leucine

20 markedly drops the redox

midpoint potential by hundreds of millivolts and disables electrontransfer from either cytochromecor FeS. But oxidation of QH2atthe Qosite proceeds to the same extent and with kinetics essentiallyidentical to the wild type, and reduction of FeS by QoH2 isunimpeded. Once FeS is reduced, oxidation of a second QoH2 isimpossible and, unlike the wild-type cytochromebc1, this knockoutis a de factoQosite single-turnover enzyme.

In the second cofactor knockout (Fig. 2c), insertion of twoalanines in the hinge region between the FeS head group and thetransmembrane anchor severely interferes with the normal move-ment of FeS, thereby locking it in the Qosite position

17. This alsoprevents communication between the Qo site and haem c1 andcytochromec, and again provides rigorous single-turnover action.But like thec1knockout, the FeS-motion knockout yields the samekinetics and extents as the wild type. Clearly, the diffusive, large-

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scale domain motion of FeS is not needed for fully competent Qosite activity17,21. The third knockout (Fig. 2d) replaces the haembHhistidineligand with an asparagine, and haem bH is lost

22, providingan alternative way to restrict the Qo site to one turnover. Butreduction of haem bL, together with reduction of FeS and haemc1, takes place with kinetics similar to that of haembHreduction.

The simultaneous knockout of two cofactors most severelystrains cytochromebc1turnover and delineates the thermodynamic

limits of Qo site action under high redox potential conditions.Pairing thebHknockout with either thec1knockout (Fig. 2e) or theFeS-motion knockout (Fig. 2f) trims the multicofactor enzyme to

just three components: Qo, FeS and haembL. Remarkably, Qositeaction has essentially the same rate of haembreduction as the wildtype. However, the extent of haembreduction is only about a thirdunder these conditions, indicating that the oxidationreductionreaction of this simple three-component system may be energeti-cally balanced and fully reversible on this timescale.

The reversibility of the system and the thermodynamicallycooperative behaviour of the b- and c-chains become obviouswhen, following the guidelines of Fig. 1b and c, we manipulatethe driving force provided to cytochromebc1by changing the pHand state of the Q pool reduction before the activation. Figure 3

shows the pH modulation of the extent of haem b reduction for wildtype and thec1knockout (Fig. 3a), and for thebHknockout and thebH c1double knockout (Fig. 3b) at both the high redox potentialcondition of the oxidized Q pool described above, and at a lowerredox potential at which the Q pool is half-reduced and the arrivalof QH2 at the Qo site is not rate-limiting. All systems become

progressively less competent as the driving force is lessened, eitherthrough raising the redox poise or through lowering the pH, whichraises the midpoint potential of the Q pool (Fig. 1b, c).

A simple equilibrium model

The progressive failure of the extent of haemb reduction is neatlyaccommodated in an equilibrium model with four simple postu-lates (Fig. 3a, b, lines, and Fig. 3ce, graphic illustrations). First,

individual redox centres have the same midpoint potentials on thecatalytic timescale as those measured in equilibrium redox titrationson a timescale of minutes (Fig. 1b). Second, the 2:1 ratio of reactioncentres to cytochromebc1monomer produces two oxidized cyto-chromesc2and one QH2per flash (ref. 9 and Fig. 3d); this postulatemay be less valid at the high pH limit of 10, where QH2productionby the QBsite in reaction centres may begin to fail. Third, Qositeredox reactions are strictly coupled so that every electron exchangedbetween the Qo site quinone and FeS is accompanied by electronexchange between quinone and haem bL (refs 23, 24). Fourth,electron transfers between Qo and FeS and haem bL, as well aselectron transfers between members of the b-chain and betweenmembers of the c-chain, continue until the redox potential of the Qpool equals the average of the redox potentials of the c- and b-chain;that is, the net driving force for the Qosite reaction is zero (refs 23,24, and Fig. 3e).

The double knockout system (Fig. 3b, black) has the least drivingforce and is the first to fail as the pH is lowered (see Fig. 1c). Whencommunication with haemsc1and c2is restored in the single bHknockout (Fig. 3b), the thermodynamically cooperative involve-ment of these haems improves cytochromebc1robustness. At highredox potential (Fig. 3b, red), simple, rapid redox equilibriumcontact with multiple oxidized redox centres in the c-chain favoursmore QH2oxidation and haembLreduction, which continues even

Figure 2Flash-activated haembreduction. Kinetics are shown for wild type (a) and

cofactor knockout combinations (bf) at pH 9.0 and at an of Ehof 250 mV to oxidize

the Q pool, FeS and haem bbeforethe flash. Haem kinetics, initiatedby QH2 diffusingfrom

the reaction centre, is uninhibited (black) or inhibited with antimycin (green), antimycin

and myxothiazol (red, left), or myxothiazol alone (red, right). Reduction of haem bH(left)

and haembL(right) is monitored by absorption change presented in milli-units of optical

density (mOD) at 560570nm and 566573 nm, respectively; the initial step reflects

reaction centre spectral contributions at these wavelengths. Red crosses indicate the

locations of knockouts and blue arrows delineate remaining electron transfer reactions.

FeS

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Figure 1 Cofactors and their energetics in R. capsulatus.a, Light-activatedR. capsulatus

initiates electron (blue) and proton (green) transfers through haems and chlorins

(squares), quinones (hexagons) and the FeS cluster (double cross) of its reaction centre

and cytochromebc1to generate DmH. The reaction centre generates oxidized

cytochromec2and hydroquinone (QH2), which diffuse to a dimeric cytochromebc1.

Oxidized cytochromec2oxidizes haemc1. Haemc1oxidizes FeS, which, by limited

diffusion, arrivesat the Qosite to oxidize QH2drawn from the pool. QoH2oxidation reduces

both FeS and haembL. Red crosses indicate the positions of cofactor knockouts. b,c, pH

dependence of cofactor equilibrium midpoint (Em) potentials (b) yields adjustable patterns

of endergonic and exergonic steps beginning at the Qosite (c). Grey areas indicate steps

inactivated by antimycin and thebHknockout.

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as the Q pool midpoint rises with lower pH, until about pH 7. Atredox potentials with the Q pool half-reduced(Fig. 3b, green), moredriving force is provided and failure is delayed until the pH is lowerthan 6. Similarly, when communication with haembHis restoredand the contribution of haemsc1andc2is denied in thec1 knockout(Fig. 3a, grey), the thermodynamic assistance of haem bHcooperates in maintaining haem b reduction until pH 6. In wildtype, both at high (Fig. 3a, blue) and low (Fig. 3a, magenta) redox

potentials, the cooperative action of the extended c- and b-chainsallows haembHreduction and transmembrane electron transfer tocontinue well below pH 6. The simple equilibrium model tracks theprogressive failure of all of the different systems.

The thermodynamic cooperativity of the b-chain apparent in thebH knockouts is likely to be enhanced by cross-dimer electrontransfer (Fig. 4). Cytochromebc1structures

2528 reveal a tunnellingdistance between the two haemsbLin the dimer that is only slightlylonger than the tunnelling distance between haembLand haembH;conservative calculation places haembLtobLelectron tunnelling attens of microseconds29. This means that whenever Qosite catalysisin one or both monomers leaves two electrons in the b-chain of thedimeric complex, tunnelling between components of the chainshould allow both electrons to doubly reduce a single Qi on amillisecond timescale.

Significantly, this redistribution of electrons can occur withoutinvolving the Qo site. In effect, this removes the strict couplingbetween two turnovers of one Qosite and one Qisite described in

the traditional double Q-cycle model30. It also helps to explain howthe first substoichiometric fraction of antimycin that binds, inhibitsnoticeably less effectively than the final fraction31,32.

Although the extent of haemb reduction is considerably modu-lated by changing the pH and by the addition and removal of redoxcentres, the reaction rate is unperturbed for the most part (Fig. 5).At high redoxpotentials when theQ pool is initiallyoxidized (Fig. 5,blue), pH has little effect on the QH2oxidation rate; under these

conditions, the process is simply limited by the diffusion of QH2from the reaction centre to cytochromebc1. At low redox potentials(Fig. 5, red), whereQH2 is already available in thepool and not rate-limiting, lowering the pH below 7 finally begins to slow haem breduction (Fig. 5, dotted line limit is 10-fold change of rate per pHunit). This drop in rate parallels the shrinking driving force for QH2to FeS and haem b L electron transfer, as determined by theequilibrium midpoint potentials (Fig. 1b).

The b- and c-chain components contribute directly and inde-pendently to the total driving force of the reaction. Thede factosingle-turnover knockouts show that the haemb and haem c1re-reduction rates are not dependent on haem bL to bH electrontransfer and Qi site action in the b-chain, as was previouslysuggested14,16,33. Independence is similarly clear when exogenouslight-activated oxidants trigger a single turnover showing no anti-mycin effect on the haem c1 re-reduction rates34. The knockoutsshow no indication of the proposed long-range effects of Qi onelectron transfer in the c-chain35, of tight coupling of FeS motion to

Figure 3Extent of flash-activated Qosite catalysis fitted to the simple equilibrium model.

Points indicate yields of haembreduction catalysed by the Qosite, lines are derived from

the equilibrium model.a, Haembreduction yields (antimycin) in wild type with the Q pool

half-reduced (magenta) or oxidized (blue), and in the c1knockout with the Q pool oxidized

(grey).b, Haembreduction yields in the bHknockout with the Q pool half-reduced (green)

or oxidized (red), and in the c1bHdouble knockout with the Q pool oxidized (black).

c, Simple equilibrium model: redox equilibration on a timescale of minutes (Eh) sets initial

equilibrium levels of reduction of the c-chain (red), Q pool (blue) and b-chain (green).

d, Flash-activated reaction centre (RC) rapidly offsets reduction levels of cytochrome c2and Q/QH2. e, Millisecondreversible Qo site catalysiscontinues untilthe Q pool potentialis

the average of the c- and b-chains. Flared reservoirs reflect nernstian redox buffering.

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electron transfer in the b-chain8,14, nor of regulation of electrontransfer competence by carefully controlled protonation states5,7,36.

Because a simple equilibrium model sufficiently explains reactionextents under an extreme range of thermodynamic and knockoutconditions, there is little reason to suppose that redox properties onthe millisecond timescale are substantially different from the equi-librium values. There is no evidence that redox states of one centreprofoundly influence the redox properties of others, and the

influence of protonation or deprotonation of a redox centre on itsaffinity for electrons is adequately reflected in the equilibrium pHdependencies of these centres.

Short-circuiting of reversible electron transfer

The short-circuit rate of haembreoxidation when Qiis inoperative(Fig. 5, purple) shows that the rapidly reversible cytochrome bc1,like the essentially irreversible reaction centre, suppresses short-circuits into the timescale of seconds, even though the methods ofsuppression must be different. Figure 6 examines structural contri-butions to physiologically reversible cytochromebc1and attendantshort-circuits. The two short-circuit reactions of Fig. 6a and binvolve oxidation of QH2by FeS and haemc1, or reduction of Q byhaemb Land haembH, and compete directly with the forward andreverse physiological reactions. However, both these short-circuitsare prevented simply by the electron tunnelling geometry ofcytochrome bc1. Haem bL and FeS are positioned close to Qo,fostering submillisecond physiological tunnelling, while the poten-tially short-circuiting haem bH and haem c1 components areconsiderably farther away, with corresponding tunnelling ratesslowed safely to a timescale of seconds. A natural consequence ofthe distant haemc1is that FeS must undergo motion between thehaem c1 and the Qo site

1719 to achieve short enough tunnellingdistances to keep electron transfer faster than the catalytic rate.Although rapid FeS motion may have a role in reassembling andrapidly refreshing the Qosite with protons and quinones to reflectthe equilibrium pH and quinone pool redox states, in itself thesimple motion does not prevent the short-circuit reactions of Fig. 6.

The three-step short-circuits of Fig. 6c and d might be minimized

with sufficiently unstable semiquinone (that is, with a small stabilityconstant,Kstab)9,24,37,38. Simple tunnelling calculations29, using crys-

tal structure distances2528 and driving force (DGo) values given by

equilibrium titrations (Fig. 1b) and a range of Kstab values forsemiquinone, indicate how unstable the semiquinone must be tosuppress short-circuits. With quinone in a position similar to theinhibitor stigmatellin and a reorganization energy for Qoelectrontransfer similar to that of QB(1.01.2 eV), aKstabvalue of less than10216 is required to slow the three-step short-circuit reactions ofFig. 6c and d to a timescale of seconds. Even smaller values(Kstab , 10

222) are required to slow the two-step short-circuits of

Fig. 6e and f.A lowKstabslows short-circuits by making some reactions, such

as haem bL to oxidized Qo electron transfer, extremely uphill;however, the physiologically productive forward and reverse reac-tions that use these same uphill steps will also be slowed. With thegeometry and energetics described above,Kstab must be greater than10210 to allow haembLto Qoelectron tunnelling on a submillise-cond timescale in reverse physiological electron transfer. Thus, thereis no single value of Kstab that will permit rapid submillisecondforward and reverse electron tunnelling and simultaneously limitshort-circuit tunnelling to the timescale of seconds.

Safe, reversible Qosite energy conversion

Nearly all proposed models58,1012,14,16 invoke redox-sensitive con-formational choreography to gate the stability of the semiquinonestate (see Supplementary information), and all fail because theyneglect or even forbid reverse reactions and do not consideroxidized Qo-mediated short-circuits. For example, the model of acatalytic switch of FeS8 supposes that FeS cannot assume the bposition at the Qosite and react with Qounless both FeS and haembL are oxidized; this avoids the short-circuits shown in Fig. 6c, e.However, this model prevents neither the short-circuit of Fig. 6f,because when haem bL reduces Qo, both FeS and haem bL areoxidized and FeS will be reduced by highly favourable electrontransfer from semiquinone,nor theshort-circuit of Fig. 6d,in whichsuccessive FeS-independent electron transfers from haembLreduceQo. Furthermore, the reverse physiological reaction, in which haembLand then FeS reduce Qoto QoH2, seems to be forbidden because

Figure 4 Intermonomer tunnelling in cytochrome bc1. After initial entry of an electron into

a b-chain (blue arrow), distances betweenbL haems in the dimer are short enough to

permit tunnelling equilibration between allbhaems and Qisites (red arrow) on a

timescale of Qosite catalysis and in a manner independent of the Qosite.

5 6 7 8 9 10

Figure 5Rates of Qi-inhibited haembreduction and reoxidation in cofactor knockouts as

a function of pH. When the Q pool is half-reduced before the flash (red), rates follow the

limiting catalytic rate, slowing at the lowest pHs where the driving force for Q osite

catalysis decreases (Fig. 1c). When the Q pool is oxidized before the flash (blue), rates

follow the rate of diffusion of QH2from the reaction centre. Haembreoxidation rates

(purple) reflect energy-wasting short-circuits; these are unaffected by added redox-

poising dyes.

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the reduced FeS is assumed not to take the b position.Any attempt to repair these models requires additional redox-

sensitive conformational gating and explicit reversibility. This ismost easily achieved by double gating of the Qo site (see Sup-plementary Information). Double gating could be based on con-trolled hydroquinone and quinone binding or on modulatedsemiquinone redox properties such asKstabto enable semiquinoneformation when FeS and haemb Lare both oxidized (physiological

forward) or both reduced (physiological reverse) and not when FeSis oxidized and haem bL reduced. Application of such gatingelements successfully allows reversibility while eliminating theshort-circuits of Fig. 6cf.

An alternative abandons the elaborations implicit in gatedsequential models and exploits the potential for reversible, genu-inely concerted electron transfer provided by the quinone redoxchemistry itself. We use concerted as a kineticterm that defines twoevents taking place without time for significant atomic rearrange-ment, in other words, within femtoseconds39. Theoretical andexperimental descriptions of kinetically concerted two-electrontransfers are developing40,41. In contrast to common sequentialmodels (Fig. 6h, bottom), this fundamentally different mechanismfor Qosite catalysis has reversible concerted two-electron transfertaking place through a transition state devoid of semiquinonecharacter (Fig. 6h, top).

The term concerted has long been used in the cytochrome bc1literature12,24,42, but it usually refers to the thermodynamic co-operativity of the Qo site reaction, in which electron transfer issequential with a transient semiquinone state that never accumu-lates enough to be observable; in this case, reduction and oxidationof reaction partners may appear concurrent. The term concertedcontinues to be used in redox-sensitive gating models15, eventhough kinetic concertedness renders such gating meaningless.

A Qosite designed for concerted catalysis must strongly destabi-

lize the semiquinone to a Kstab value of less than 10222 to make

sequential short-circuits through semiquinone energeticallyunfavourable enough to slow them to seconds. At the same time,the availability of proton donors and acceptors is essential43,44. It isthe combination of these circumstances that can favour concertedtwo-electron transfer reactions over sequential reactions39,45.Although a concerted mechanism will probably have a largercontribution to the kinetic barrier from increased reorganization

energy, this maybe more than compensatedby themarkedlysmallerDG o contribution to the barrier (DG oconcerted near zero ,,DGosequential). Most of the thermal energy required to reach aconcerted Qo transition state presumably would be invested inreorganization in the form of occasionally synchronous movementof protons towards or away from the quinone oxygens, with thecorresponding changes in bond lengths in the quinone.

The concerted model is silent on the exact sequence of protona-tion events relative to the two near simultaneous electron transfers,although it is likely that reorganization of the Qosite moves at leastone proton into an intermediate, non-equilibrium position toachieve the lowest energy transition state for rapid two-electrontransfer. In the reversible concerted model, the only short-circuitreaction that remains (Fig. 6g) is over the much longer distance of23 A directly between haem bL and FeS, which, like the samedistancecharge recombination in reaction centres, should have atunnelling time on the scale of seconds29. Indeed, the short-circuitrate observed in cytochrome bc1 (Fig. 5, purple) matches thispredicted rate of seconds.

The models developed here show that efficient redox energycoupling in cytochrome bc1 is assured by redox cofactor arrange-ment and different quinone chemistry at the Qoand Qisites. Redoxcofactors engaging in productive forward and reverse electrontransfers are separated by tunnelling distances of less than about14 A. Within this limit, thermodynamically cooperative interactions

Figure 6Qosite catalysis and short-circuits in physiologically reversible cytochromebc1.

af, The geometry and spacing of cofactors2528 is organized to promote forward and

reverse physiological electron transfers (a,b, solid arrows) and to prevent some short-

circuits (a,b, broken arrows) but not others (cf). The order of electron transfers in

models involvingsemiquinone intermediates is blue,red andthen green. g, A short-circuit

that even a reversible concerted model cannot avoid involves long-distance and safely

slow, direct electron tunnelling between haembLand FeS.h, Concerted (top) and

sequential (bottom) mechanisms differ considerably in the reaction energy surface profile

during forward and reverse Qosite catalysis.

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through the extended redox chains sustain mechanistically robustfunction over a broad range of redox and pH conditions. Unpro-ductive electron transfers generally face longer distances. In the Qosite, where such long-distance suppression of unproductive reac-tions is not possible because the same centres participate inproductive electron transfer, reversible double gating of sequentialreactions or a concerted ubiquinone redox chemistry is required toavoid semiquinone-mediated short-circuits. The Qosite design to

suppress or even exclude semiquinone joins the cross-dimer elec-tron transfer action to sweep the b-chain of reduced haem b,diminishing the potential for the generation of damaging radicalsand reactive oxygen species in normally functioning mitochon-dria46. A

Methods

Cofactor knockouts

The single mutations in haem c1and the FeS subunit ofR. capsulatuscytochromebc1,M183L and the 2Ala insertion, have been described17,20. The single H212N mutation inthe cytochrome b subunit results inthe selective loss ofhaem bH andtheretention of haembLin a manner similar to that reported in studies ofRhodobacter sphaeroidescytochromebc1(ref. 22, and T. Dogerthy, K. Gray and F. Daldal, unpublished data). We created thedouble mutations M183L/H212N and 2Ala/H212N by ligating appropriate restrictionfragments derived from plasmids carrying single mutations, and we introduced them intoa suitable genetic background as described47.

Membranes, titrations and kinetics

Chromatophore membrane preparation, dark equilibrium redox titrations of FeS andhaem b, and light-induced time-resolved kinetics in the presence of valinomycin weredoneas described9,20,48,49. Theextent of haemb reductionwas simulated with Mathematica(Wolfram Research) using the four postulates described in the text.

Received 11 August; accepted 14 November 2003; doi:10.1038/nature02242.

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Supplementary Informationaccompanies the paper onwww.nature.com/nature.

Acknowledgements This work was supported by grants fromthe National Institutes of Health to

P.L.D. and F.D.

Competing interests statement The authors declare that they have no competing financial

interests.

Correspondenceand requests for materials should be addressed to P.L.D.

([email protected]).

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